Modeling Top of Atmosphere Radiance over Heterogeneous Non-Lambertian Rugged Terrain

Abstract

Topography affects the fraction of direct and diffuse radiation received on a pixel and changes the sun–target–sensor geometry, resulting in variations in the observed radiance. Retrieval of surface–atmosphere properties from top of atmosphere radiance may need to account for topographic effects. This study investigates how such effects can be taken into account for top of atmosphere radiance modeling. In this paper, a system for top of atmosphere radiance modeling over heterogeneous non-Lambertian rugged terrain through radiative transfer modeling is presented. The paper proposes an extension of “the four-stream radiative transfer theory” (Verhoef and Bach 2003, 2007 and 2012) mainly aimed at representing topography-induced contributions to the top of atmosphere radiance modeling. A detailed account for BRDF effects, adjacency effects and topography effects on the radiance modeling is given, in which sky-view factor and non-Lambertian reflected radiance from adjacent slopes are modeled precisely. The paper also provides a new formulation to derive the atmospheric coefficients from MODTRAN with only two model runs, to make it more computationally efficient and also avoiding the use of zero surface albedo as used in the four-stream radiative transfer theory. The modeling begins with four surface reflectance factors calculated by the Soil–Leaf–Canopy radiative transfer model SLC at the top of canopy and propagates them through the effects of the atmosphere, which is explained by six atmospheric coefficients, derived from MODTRAN radiative transfer code. The top of the atmosphere radiance is then convolved with the sensor characteristics to generate sensor-like radiance. Using a composite dataset, it has been shown that neglecting sky view factor and/or terrain reflected radiance can cause uncertainty in the forward TOA radiance modeling up to 5 (mW/m2·sr·nm). It has also been shown that this level of uncertainty can be translated into an over/underestimation of more than 0.5 in LAI (or 0.07 in fCover) in variable retrieval.

Keywords

• top of atmosphere radiance
• coupled radiative transfer model
• SLC
• MODTRAN
• non-Lambertian
• rugged terrain
• sky view factor
• terrain reflected radiance